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In this paper, we prove that a linear block code with girth 2( t +1) is a  t -sequential-recovery locally repairable codes (LRCs) with locality  r  if its parity-check matrix has column weight at least 2 and row weight at most  r +1. This gives a new connection between sequential-recovery LRCs and linear block codes. We also derive that the repair time of the  t -sequential-recovery LRCs from the linear block codes by this connection is at most &#x2308; t /2&#x2309;.

Girth-based sequential-recovery LRCs